Chest cavities aren't especially space-constrained, and another commenter mentioned that electrodes wear out fairly quickly (single-digit years), so it appears that a fixed non-rechargeable battery has enough capacity to last the lifetime of the device.

Wireless charging (for a pacemaker) has the issue that you've got to push the energy through quite a lot of flesh, with consequent efficiency and heat issues.

Wireless charging is absolutely an option for other devices implanted closer to the skin, though.

The issue being rather close to my heart, I'd rather have a single-use 7-year battery + full modern replacement of unit, than have to fiddle with periodic recharging just to prolong use of aging technology. Nobody much wants their life relying on >10 year old computers. (Remember: it's already "old technology" when you first get it implanted.)

I think the main problem is the giant meat sack sitting between the charging pad and battery :)